Optimal Financing Decisions of Two Cash-Constrained Supply Chains with Complementary Products
Abstract
:1. Introduction
1.1. Motivation
1.2. Review of Literature
- For our government, there are a lot of works that can be done for them, for instance, to conduct the initial public offering (IPO) and stock exchange [26], to set up some government connections with SMEs [27,28], to increase more and more affordable local financing supply [29], to produce a demonstration effect whereby successful SMEs supported by donor-backed programs [29], to implement some financial aid programs that focus on SME scarce availability of collateral [30].
- For SMEs, there are also several ways to solve their financing problems, for example, to increase enterprises’ internal capital efficiency to improve credit constraints [31,32], to seek some venture capitals [33], to get guarantee loans [34,35,36,37,38,39,40,41,42], to obtain pledge loans [43,44,45], to apply collateral loans [40,46,47,48,49,50]. In fact, it is not easy for SMEs to find some suitable guarantees for their financing loans, but it will get easier if SMES and their potential guarantees are members of the same supply chain alliance.
- For a supply chain [51], there exist supply chain effects of bankruptcy due to the financing guarantee, but there are enough incentives for the leader enterprises of a supply chain to help other members to get enough loans in order to preserve competition, improving supply chain efficiency and providing support for the exclusivity rule [52,53]. In some supply chain finance systems, the optimal expected profit under either financing mode would be higher than that in the case of no capital constraint or capital constrained without financing [54,55]. A lot of literatures showed that financing models can have great effects on the operation management of the supply chain members. [56,57,58,59,60,61,62,63,64]
1.3. Contributions
- We propose financing models by extending financing decision participants from a single supply chain [66] into two parallel supply chains with complementary products.
- With regard to all decision participants of two parallel supply chains with complementary products, we prove the best financing way for them is to make a joint financing decision.
1.4. Framework
2. Assumptions, Abbreviations and Notations
2.1. Assumptions
- Assumption 1: Each supply chain consists only of two players, i.e., a manufacturer and a retailer, as shown in Figure 1.
- Assumption 2: All players, lender, manufacturer and retailer, are all rational.
- Assumption 3: Manufacturers cannot afford all their desired production costs only with their initial capitals. Similarly, retailers’ initial capitals cannot fully cover their desired purchasing costs. Only if manufacturers and retailers have cash constraint problems, they will make their effort to get more cash. One of the best choices for manufacturers and retailers is to get some financing loans.
- Assumption 4: Lending rates remained unchanged. That is, the lending rate does not depend on financing amount, manufactures and retailers can get the loan with the same rate.
- Assumption 5: There is no defective product.
- Assumption 6: In dual supply chains, manufacturers are dominant, and retailers’ initial capitals are near zero. The probability for manufacturers and retailers to get loan by themselves is less than 1, but the probability for retailers is less than manufactures’.
2.2. Notation
3. A Financing Model of a Single Supply Chain
3.1. Independent Financing Decisions
3.1.1. Independent Financing Decisions of MA
- (1)
- If the lender gives MA a loan, its profit function is
- (2)
- If the lender refuses to give MA a loan, its profit function is
3.1.2. Independent financing decisions of RA
- If RA can get a loan from its lender, its profit function can be determined by:
- If RA failed to get a loan, its profit function can be determined by:
3.1.3. Analyses on Independent Financing Decisions
3.2. Joint Financing Decisions of SCA
3.2.1. A Joint Financing Model
- If the lender provides a loan to SCA, profit functions of MA and RA are
- If the lender refused their joint financing contract, the quantity equilibrium of MA's production and RA’s order satisfies . Therefore, their profit functions are written as
3.2.2. Analyses on Joint Financing Decisions
3.3. Comparisons of Independent Decisions and Joint Financing Decisions of SCA
- For MA, One can get its expected profit with the independent financing decision as shown in Equation (30) and its expected profit with the joint financing decision as follows.So their difference is
- For RA, it is easy to get its expected profits with the independent decisions and joint financing decisions, respectively, as follows:
4. A Joint Financing Model of SCA and SCB
4.1. A Joint Financing Model of SCA and SCB
4.2. Comparison of Different Financing Decisions of SCA and SCB
5. Numerical Study
5.1. Simulations for the Financing Model of a Single Supply Chain
5.2. Simulations for the Joint Financing Model of SCA and SCB
- Both MA and RA can obtain more profits with joint financing decisions than those with independent financing decisions.
- Bigger are cross-price sensitivity coefficients, higher are profits of MA and RA with independent financing decisions and joint financing decisions.
6. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Abbreviations
SMEs | Small and medium enterprises |
SCA | The supply chain with the product A |
SCB | The supply chain with the product B |
MA | The manufacturer with product A |
MB | The manufacturer with product B |
RA | The retailer with product A |
RB | The retailer with product B |
MDA | The market demand for product A |
MDB | The market demand for product B |
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Notation | Description | Unit |
---|---|---|
, | Initial capitals of MA and MB, respectively. | Million dollar |
, | Initial capitals of RA and RB, respectively. | Million dollar |
, | Financing amounts of MA and MB, respectively. | Million dollar |
, | Financing amounts of RA and RB, respectively. | Million dollar |
, | Production quantities of MA and MB, respectively. | Standard quantity unit(SQU) |
, | Order quantities of RA and RB, respectively. | SQU |
, | Unit production costs of products A and B, respectively. | Million dollar/SQU |
, | Salvage values of unsold products A and B, respectively. | Million dollar |
, | Retailers’ purchase prices of the products A and B, respectively. | Million dollar/SQU |
, | Unit sales prices of the products A and B, respectively. | Million dollar/SQU |
lending rates | Percentage/year | |
deposit rates | Percentage/year | |
, | probability for manufacturers and retailers to get loan by themselves, respectively | Null |
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Li, Y.; Chen, T.; Xin, B. Optimal Financing Decisions of Two Cash-Constrained Supply Chains with Complementary Products. Sustainability 2016, 8, 429. https://doi.org/10.3390/su8050429
Li Y, Chen T, Xin B. Optimal Financing Decisions of Two Cash-Constrained Supply Chains with Complementary Products. Sustainability. 2016; 8(5):429. https://doi.org/10.3390/su8050429
Chicago/Turabian StyleLi, Yuting, Tong Chen, and Baogui Xin. 2016. "Optimal Financing Decisions of Two Cash-Constrained Supply Chains with Complementary Products" Sustainability 8, no. 5: 429. https://doi.org/10.3390/su8050429